Related papers: Towards Minimal Fault-tolerant Error-Correction Se…
We introduce a framework called spacetime concatenation for fault-tolerant compilation of syndrome extraction circuits of stabilizer codes. Spacetime concatenation enables efficient compilation of syndrome extraction circuits into dynamical…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
State-of-the-art noisy intermediate-scale quantum computers require low-complexity techniques for the mitigation of computational errors inflicted by quantum decoherence. Symmetry verification constitutes a class of quantum error mitigation…
Recent advances in quantum error-correction (QEC) have shown that it is often beneficial to understand fault-tolerance as a dynamical process, a circuit with redundant measurements that help correct errors, rather than as a static code…
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple…
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic…
Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hausdorff dimension $2+\epsilon$, which admits a fault-tolerant non-Clifford CCZ gate. We investigate the performance of such FSCs as…
We develop novel protocols for generating loss-tolerant quantum codes; these are central for safeguarding information against qubit losses, with most crucial applications in quantum communications. Contrary to current proposals, our method…
We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit…
Reducing space and time overheads of fault-tolerant quantum computation (FTQC) has been receiving increasing attention as it is crucial for the development of quantum computers and also plays a fundamental role in understanding the…
We introduce a construction for protocols for fault-tolerant quantum computing based on code concatenation and transversal gates. These protocols can be interpreted as families of quantum circuits of low-weight stabilizer measurements…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an…
We discuss how the presence of gauge sub-systems in the Bacon-Shor code [D. Bacon, Phys. Rev. A 73, 012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
Fault-tolerant quantum computers compose elements of a discrete gate set in order to approximate a target unitary. The problem of minimising the number of gates is known as gate-synthesis. The approximation error is a form of coherent…